Question: Emily's quiz scores so far are: 92, 95, 87, 89 and 100. What score does she need to get on the sixth quiz to make the arithmetic mean of the six scores equal 93?
Explanation: Subtract 90 from every score to simplify the arithmetic.  For the average of 6 scores to be 3, their sum must be $6\times3=18$.  The sum of her first five scores is $2+5-3-1+10=13$, so the sixth score should be $18-13=5$.  Adding 90 back, her score should be $\boxed{95}$.